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प्रश्न
ABCD is parallelogram and E is a point on BC. If the diagonal BD intersects AE at F, prove that AF × FB = EF × FD.
उत्तर
We have:
∠𝐴𝐹𝐷= ∠𝐸𝐹𝐵 (𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙𝑙𝑦 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑛𝑔𝑙𝑒𝑠)
∵ DA || BC
∴ ∠𝐷𝐴𝐹= ∠𝐵𝐸𝐹 (𝐴𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑒 𝑎𝑛𝑔𝑙𝑒𝑠)
Δ DAF ~ Δ BEF (AA similarity theorem)
⟹ 𝐴𝐹𝐸𝐹=𝐹𝐷𝐹𝐵
Or, AF × FB = FD × EF
This completes the proof
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